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Eulers Relationship

  1. Apr 16, 2010 #1
    May be it's a stupid question but I can't figure it out.

    according to Eulers Relationship:
    ej[tex]\alpha[/tex]=cos[tex]\alpha[/tex]+jsin[tex]\alpha[/tex]

    on the other hand I have equation:
    Vt=V0cos wt
    and it can be rewritten as:
    Vt=V0ejwt

    where V is voltage in AC (see link below)
    http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/impcom.html" [Broken]

    In this case cos wt is at the place of cos[tex]\alpha[/tex], but what I can't understand is, where did jsin [tex]\alpha[/tex] go?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 16, 2010 #2

    Hurkyl

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    I quote, with added emphasis:

     
  4. Apr 16, 2010 #3
    that is what I am asking about. and what happens with the imaginary part? And if we can simply neglect it, then why?
     
  5. Apr 16, 2010 #4
  6. Apr 16, 2010 #5

    Hurkyl

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    Two miniature ideas to pay attention to:

    1. Re(eix) is often more convenient than cos(x)
    2. Im(eix) may tell you something else that's interesting
     
  7. Apr 17, 2010 #6
    After searching through the web, only thing I could conclude and understand is that after several transformation from ejx=cosx+jsinx I come to:
    cosx=(eix+e-ix)/2
    but, what I can't understand is the equation:
    (eix+e-ix)/2=R{eix}
    well, the wikipedia says that:
    see: http://en.wikipedia.org/wiki/Electrical_impedance" [Broken] Validity of comples representation.

    May be it is simple math, but I can't understand if there is any special meaning of curly brackets.
     
    Last edited by a moderator: May 4, 2017
  8. Apr 17, 2010 #7

    HallsofIvy

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    If z= x+ iy then the real part of z is Rz= x.

    It's exactly the same thing as if I say "the x-coordinate of the point (2, 3) is 2".

    That's all it is- it's not the { } that is important but the "R".

    If [itex]e^{j\omega t}= cos(\omega t)+ j sin(\omega t)[/itex] then the "real part" is [itex]cos(\omega t)[/itex] and the "imaginary part' is [itex]sin(\omega t)[/itex] (notice that both "real part" and "imaginary part" of a complex number are real numbers).

    [itex]R(e^{j\omega t}) cos(\omega t)[/itex] and [itex]I(e^{j\omega t}) sin(\omega t)[/itex].
     
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